com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection

Class ConjugateGradient

java.lang.Object

com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection.ConjugateGradient

All Implemented Interfaces:

Minimizer<C2OptimProblem,IterativeMinimizer<Vector>>, Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>, MultivariateMinimizer<IterativeMinimizer<Vector>>, java.io.Serializable

Direct Known Subclasses:

FletcherReeves

public class ConjugateGradient
extends SteepestDescent

A conjugate direction optimization method is performed by using sequential line search along directions that bear a strict mathematical relationship to one another. In particular, this conjugate-gradient method generates a new search direction by adding a vector β_kd_k to the negative gradient -g_k+1. The algorithm was originally developed for quadratic problems. For convex quadratic problems, the algorithm converges in n iterations, where n is the number of variables. It still has good convergence properties when applied to non-quadratic problems.

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Theorem 6.4, Algorithm 6.2," Practical Optimization: Algorithms and Engineering Applications."
• Wikipedia: Conjugate gradient method

, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

SteepestDescent.SteepestDescentImpl

Field Summary

Fields inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

epsilon, maxIterations

Constructor Summary

Constructors

Constructor and Description
ConjugateGradient(double epsilon, int maxIterations) Construct a multivariate minimizer using the Conjugate-Gradient method.

Method Summary

Modifier and Type	Method and Description
IterativeMinimizer<Vector>	solve(C2OptimProblem problem) Solve a minimization problem with a C2 objective function.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ConjugateGradient

public ConjugateGradient(double epsilon,
                         int maxIterations)

Construct a multivariate minimizer using the Conjugate-Gradient method.

Parameters:

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

maxIterations - the maximum number of iterations

Method Detail

solve

public IterativeMinimizer<Vector> solve(C2OptimProblem problem)
                                 throws java.lang.Exception

Description copied from class: SteepestDescent

Solve a minimization problem with a C² objective function.

Specified by:

solve in interface Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>

Specified by:

solve in class SteepestDescent

Parameters:

problem - a minimization problem with a C² objective function

Returns:

a minimizer

Throws:

java.lang.Exception - when there is an error solving the problem